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Hierarchical Bayesian CMB component separation with the No-U-Turn Sampler

Grumitt, R. D. P. and Jew, Luke R. P. and Dickinson, C. (2020) Hierarchical Bayesian CMB component separation with the No-U-Turn Sampler. Monthly Notices of the Royal Astronomical Society, 496 (4). pp. 4383-4401. ISSN 0035-8711.

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In this paper, we present a novel implementation of Bayesian cosmic microwave background (CMB) component separation. We sample from the full posterior distribution using the No-U-Turn Sampler (NUTS), a gradient-based sampling algorithm. Alongside this, we introduce new foreground modelling approaches. We use the mean shift algorithm to define regions on the sky, clustering according to naively estimated foreground spectral parameters. Over these regions we adopt a complete pooling model, where we assume constant spectral parameters, and a hierarchical model, where we model individual pixel spectral parameters as being drawn from underlying hyperdistributions. We validate the algorithm against simulations of the LiteBIRD and C-Band All-Sky Survey (C-BASS) experiments, with an input tensor-to-scalar ratio of r = 5 × 10⁻³. Considering multipoles 30 ≤ ℓ < 180, we are able to recover estimates for r. With LiteBIRD-only observations, and using the complete pooling model, we recover r = (12.9 ± 1.4) × 10⁻³. For C-BASS and LiteBIRD observations we find r = (9.0 ± 1.1) × 10⁻³ using the complete pooling model, and r = (5.2 ± 1.0) × 10⁻³ using the hierarchical model. Unlike the complete pooling model, the hierarchical model captures pixel-scale spatial variations in the foreground spectral parameters, and therefore produces cosmological parameter estimates with reduced bias, without inflating their uncertainties. Measured by the rate of effective sample generation, NUTS offers performance improvements of ∼10³ over using Metropolis–Hastings to fit the complete pooling model. The efficiency of NUTS allows us to fit the more sophisticated hierarchical foreground model that would likely be intractable with non-gradient-based sampling algorithms.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper ItemPYSM software package
Grumitt, R. D. P.0000-0001-9578-6111
Dickinson, C.0000-0002-0045-442X
Additional Information:© 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2020 June 22. Received 2020 May 29; in original form 2019 October 30. The authors would like to thank David Alonso for useful comments on a draft of this paper. RDPG acknowledges support from an STFC studentship. CD acknowledges support from an ERC Starting (Consolidator) Grant (no. 307209) and an STFC Consolidated Grant (ST/P000649/1). DATA AVAILABILITY. The simulated data used in this study were generated using the PYSM software package, which can be found at
Funding AgencyGrant Number
European Research Council (ERC)307209
Science and Technology Facilities Council (STFC)ST/P000649/1
Subject Keywords:methods: data analysis, methods: statistical, cosmic background radiation, cosmology: observations, radio continuum: general
Issue or Number:4
Record Number:CaltechAUTHORS:20201022-161608802
Persistent URL:
Official Citation:R D P Grumitt, Luke R P Jew, C Dickinson, Hierarchical Bayesian CMB component separation with the No-U-Turn Sampler, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 4, August 2020, Pages 4383–4401,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106238
Deposited By: George Porter
Deposited On:23 Oct 2020 14:27
Last Modified:23 Oct 2020 15:22

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